Method for estimating polarization voltage of secondary cell, method and device for estimating remaining capacity of secondary cell, battery pack system, and vehicle

ABSTRACT

There is provided a battery pack system with enhanced estimation accuracies of a polarization voltage and a remaining capacity of a secondary battery. A polarization voltage calculation section  108  calculates a polarization voltage Vpol from a filtered variation LPF (ΔQ) of an accumulated capacity with reference to a look-up table (LUT)  1081 . An electromotive force calculation section  113  subtracts the polarization voltage Vpol from an effective no-load voltage V0 OK  to determine a battery electromotive force Veq. A remaining capacity estimation section  114  estimates a remaining capacity SOC from the battery electromotive force Veq with reference to a look-up table (LUT)  1141.

TECHNICAL FIELD

The present invention relates to a method for estimating the remainingcapacity (SOC: State of Charge) of a secondary battery such as anickel-metal hydride (Ni-MH) battery to be mounted as a power source fora motor and a driving source for various loads, in motor-driven vehiclessuch as a pure electric vehicle (PEV), a hybrid electric vehicle (HEV),a hybrid vehicle with a fuel cell and a battery, or the like.

BACKGROUND ART

Conventionally, in an HEV, when an output from an engine is large withrespect to motive power required for driving, an electric generator isdriven with surplus motive power to charge a secondary battery. On theother hand, when an output from an engine is small, a motor is drivenwith the electric power from a secondary battery to output supplementarymotive power. In this case, a secondary battery is discharged. When asecondary battery is mounted on an HEV or the like, it is necessary tomaintain an appropriate operation state by controlling suchcharging/discharging, etc.

For this purpose, the voltage, current, temperature, and the like of asecondary battery are detected, and the remaining capacity (hereinafter,abbreviated as an “SOC”) of the secondary battery is estimated bycomputation, whereby an SOC is controlled so as to optimize the fuelconsumption efficiency of a vehicle. Furthermore, at this time, in orderto allow a power assist based on motor driving during acceleration to beoperated and to allow energy to be collected (regenerative braking)during deceleration with good balance, an SOC level is controlled asfollows. Generally, in order to set an SOC to be, for example, in arange of 50% to 70%, when the SOC decreases to, for example, 50%,control for excess charging is performed. On the other hand, when theSOC increases to, for example, 70%, control for excess discharging isperformed. Thus, it is attempted to approximate the SOC to the center ofcontrol.

In order to control the SOC exactly, it is necessary to estimate exactlythe SOC of a secondary battery that is being charged/discharged.Examples of such a conventional method for estimating an SOC include thefollowing two kinds of methods.

(1) A charging/discharging current is measured. The value of the current(having a minus sign in the case of charging, and having a plus sign inthe case of discharging) is multiplied by a charging efficiency. Themultiplied values are accumulated over a certain period of time tocalculate an accumulated capacity. Then, an SOC is estimated based onthe accumulated capacity.

(2) A plurality of data sets of charging/discharging currents andterminal voltages of a secondary battery corresponding thereto aremeasured and stored. A primary approximate line (voltage V-current Iapproximate line) is obtained from the data sets by least squares, and avoltage value (V intercept of a V-I approximate line) corresponding to acurrent value 0 (zero) is calculated as a no-load voltage (V0). Then, anSOC is estimated based on the no-load voltage V0.

Furthermore, when a secondary battery is charged/discharged, apolarization voltage is generated with respect to a batteryelectromotive force. More specifically, a voltage increases duringcharging, whereas a voltage decreases during discharging. This change iscalled a polarization voltage. In the case of estimating an SOC from avoltage as in the above-mentioned method (2), in the case of estimatingan increase and a decrease in a voltage during a predetermined time, andin the case of obtaining electric power that can be input/output duringa predetermined time, it is necessary to grasp a polarization voltageexactly.

In general, as a method for estimating a polarization voltage, a primaryregression line is obtained from a plurality of current and voltagedata, the slope of the line is set to be a polarization resistance(component resistance, reaction resistance, and diffusion resistance),and the polarization resistance is multiplied by a current to obtain apolarization voltage.

However, the above-mentioned two kinds of conventional SOC estimationmethods have the following problems.

First, in the case of the SOC estimation method based on an accumulatedcapacity in the above method (1), a charging efficiency required foraccumulating current values depends upon an SOC value, a current value,a temperature, and the like. Therefore, it is difficult to find acharging efficiency suitable for these various kinds of conditions.Furthermore, in the case where a battery is sitting left, aself-discharge amount during that time cannot be calculated. For thesereasons and the like, the difference between the true value of an SOCand the estimated value thereof increases with the passage of time.Therefore, in order to eliminate this, it is necessary to performcomplete discharging or full charging to initialize the SOC.

However, in the case where a secondary battery is mounted on an HEV,when complete discharging is performed, the secondary battery cannotsupply electric power, which becomes a burden on an engine. Therefore,it is necessary to initialize an SOC after stopping a vehicle at acharging site and the like and completely discharging the secondarybattery, or after charging the secondary battery over a predeterminedperiod of time until it is fully charged. Thus, in the case of theapplication to an HEV, it is impossible to perform completecharging/discharging during driving of a vehicle so as to initialize anSOC. Furthermore, periodically performing complete charging/dischargingof a secondary battery mounted on an HEV is inconvenient for a user, andalso becomes a burden on the user.

Next, in the case of the SOC estimation method based on a no-loadvoltage in the above method (2), first, a V intercept of a V-Iapproximate line after large discharging becomes relatively low, and a Vintercept of the V-I approximate line after large charging becomesrelatively high. Thus, a no-load voltage is varied even at the same SOC,depending upon the past history of a charging/discharging current. Thischange is caused by a polarization voltage. Accordingly, the no-loadvoltage that is a V intercept of a V-I approximate line is variedbetween a charging direction and a discharging direction, due to thefactor of a polarization voltage. Because of this, the difference involtage results in an estimation error of an SOC. Furthermore, adecrease in voltage due to a memory effect and leaving a batterysitting, battery degradation, and the like also cause an estimationerror of an SOC.

Furthermore, according to the above-mentioned conventional method forestimating a polarization voltage, when a polarization voltage isobtained from a polarization resistance, a reaction resistance due tothe reaction between an active material of a battery and an interface ofan electrolyte solution and a diffusion resistance due to the reactionin active materials, between active materials, and in an electrolytesolution, included in a polarization resistance, cannot be estimatedsufficiently. Therefore, the accuracy of an estimated polarizationvoltage is unsatisfactory. Accordingly, it is not practical to use ano-load voltage in the above method (2) for correction, in order toobtain a battery electromotive force for estimating an SOC.

DISCLOSURE OF INVENTION

The present invention has been achieved in view of the above problems,and its object is to provide a method for estimating a polarizationvoltage of a secondary battery with high accuracy; a method andapparatus for estimating an SOC with high accuracy based on theestimation of a polarization voltage, without periodically performingcomplete charging/discharging of a secondary battery to initialize theSOC; a battery pack system with a computer system (electronic controlunit for a battery (battery ECU)) mounted thereon for performingprocessing in the method; and a motor-driven vehicle with the batterypack system mounted thereon.

In order to achieve the above-mentioned object, a first method forestimating a polarization voltage of a secondary battery according tothe present invention includes the steps of: measuring a current flowingthrough a secondary battery; calculating an accumulated capacity basedon the measured current; obtaining a variation of the calculatedaccumulated capacity during a predetermined period of time; andobtaining a polarization voltage based on the variation of theaccumulated capacity.

In order to achieve the above-mentioned object, a second method forestimating a polarization voltage of a secondary battery according tothe present invention includes the steps of: measuring a current flowingthrough a secondary battery used in an intermediately charged state as apower source for a motor and a driving source for a load; calculating anaccumulated capacity based on the measured current; obtaining avariation of the calculated accumulated capacity during a predeterminedperiod of time; and obtaining a polarization voltage based on thevariation of the accumulated capacity.

According to the above-mentioned method for estimating a polarizationvoltage, a polarization voltage is obtained based on the variation ofthe accumulated capacity, instead of estimating the polarization voltagebased on a polarization resistance with unsatisfactory estimationaccuracy, including a reaction resistance and a diffusion resistance,whereby the polarization voltage can be estimated with high accuracy.

It is preferable that the first and second methods for estimating apolarization voltage of a secondary battery further include the step ofsubjecting the obtained variation of the accumulated capacity to timedelay processing.

According to the above method, the polarization voltage having a delaytime with respect to the variation of the accumulated capacity can beestimated following the variation of the accumulated capacity in realtime.

Furthermore, in the first and second methods for estimating apolarization voltage of a secondary battery, it is preferable that thevariation of the accumulated capacity is subjected to averagingprocessing by filtering as well as the time delay processing.

According to the above method, a fluctuation component of theaccumulated capacity that is not required for calculating a polarizationvoltage can be reduced.

Furthermore, in the first and second methods for estimating apolarization voltage of a secondary battery, it is preferable thatcharacteristics of a polarization voltage with respect to the variationof the accumulated capacity with a temperature being a parameter arepreviously obtained, and a polarization voltage is obtained withreference to a look-up table or a formula storing the characteristics.

According to the above method, a polarization voltage can be obtainedeasily with good accuracy, even with respect to a temperature change ina battery.

Furthermore, in the first and second methods for estimating apolarization voltage of a secondary battery, the secondary battery is anickel-metal hydride secondary battery.

In order to achieve the above-mentioned object, a first battery packsystem according to the present invention includes a computer system forperforming the first or second method for estimating a polarizationvoltage of a secondary battery and a secondary battery.

In order to achieve the above-mentioned object, a battery pack systemincluding a computer system for performing the second method forestimating a polarization voltage of a secondary battery and a secondarybattery is mounted on a first motor-driven vehicle according to thepresent invention.

According to the above configuration, the battery pack system on which abattery ECU, for example, is mounted as a computer system can estimate apolarization voltage with good accuracy.

In order to achieve the above-mentioned object, a first method forestimating a remaining capacity of a secondary battery according to thepresent invention includes the steps of: measuring a data set of acurrent flowing through a secondary battery, and a terminal voltage ofthe secondary battery corresponding to the current to obtain a pluralityof the data sets; calculating a voltage value in a case where a currentvalue is zero based on the obtained plurality of data sets bystatistical processing as a no-load voltage; calculating an accumulatedcapacity based on the measured current; obtaining a variation of thecalculated accumulated capacity during a predetermined period of time;obtaining a polarization voltage based on the variation of theaccumulated capacity; subtracting the polarization voltage from theno-load voltage to calculate an electromotive force of the secondarybattery; and estimating a remaining capacity of the secondary batterybased on the calculated electromotive force.

In order to achieve the above-mentioned object, a second method forestimating a remaining capacity of a secondary battery according to thepresent invention includes the steps of: measuring a data set of acurrent flowing through a secondary battery used in an intermediatelycharged state as a power source for a motor and a driving source for aload, and a terminal voltage of the secondary battery corresponding tothe current to obtain a plurality of the data sets; calculating avoltage value in a case where a current value is zero based on theobtained plurality of data sets by statistical processing as a no-loadvoltage; calculating an accumulated capacity based on the measuredcurrent; obtaining a variation of the calculated accumulated capacityduring a predetermined period of time; obtaining a polarization voltagebased on the variation of the accumulated capacity; subtracting thepolarization voltage from the no-load voltage to calculate anelectromotive force of the secondary battery; and estimating a remainingcapacity of the secondary battery based on the calculated electromotiveforce.

According to the above method for estimating a remaining capacity, sincethe estimation accuracy of a polarization voltage is satisfactory, thecalculation accuracy of a battery electromotive force (equilibriumpotential) obtained by subtracting a polarization voltage from a no-loadvoltage is enhanced, which enables an SOC to be estimated with highaccuracy.

Furthermore, an SOC can be estimated based on an equilibrium potential,so that an SOC after self-discharging due to the leaving of a batteryfor a long period of time and the like also can be estimated, whichmakes it unnecessary to initialize the SOC periodically.

It is preferable that the first and second methods for estimating aremaining capacity of a secondary battery further include the step ofsubjecting the obtained variation of the accumulated capacity to timedelay processing.

According to the above method, a polarization voltage having a delaytime with respect to the variation of the accumulated capacity can beestimated following the variation of the accumulated capacity in realtime.

In this case, it is preferable that a polarization voltage is obtainedby multiplying the variation of the accumulated capacity subjected tothe time delay processing by a predetermined coefficient.

According to the above method, a polarization voltage can be calculatedeasily.

Furthermore, in the first and second methods for estimating a remainingcapacity of a secondary battery, it is preferable that the variation ofthe accumulated capacity is subjected to averaging processing byfiltering as well as the time delay processing.

According to the above method, a fluctuation component of theaccumulated capacity that is not required for calculating a polarizationvoltage can be reduced.

Furthermore, it is preferable that the first and second methods forestimating a remaining capacity of a secondary battery further includethe step of subjecting a polarization voltage to time delay processing.

According to the above method, the remaining capacity having a delaytime with respect to a polarization voltage can be estimated followingthe polarization voltage in real time.

In this case, it is preferable that averaging processing by filtering isperformed as well as time delay processing.

According to the above method, a fluctuation component of thepolarization voltage that is not required for estimating a remainingcapacity can be reduced.

Furthermore, it is preferable that the first and second methods forestimating a remaining capacity of a secondary battery further includethe step of subjecting both the variation of the accumulated capacityand the polarization voltage to time delay processing.

Furthermore, in the first and second methods for estimating a remainingcapacity of a secondary battery, it is preferable that characteristicsof a polarization voltage with respect to the variation of theaccumulated capacity with a temperature being a parameter are previouslyobtained, and a polarization voltage is obtained with reference to alook-up table or a formula storing the characteristics.

According to the above method, a polarization voltage can be obtainedeasily with good accuracy, even with respect to a temperature change ina battery.

Furthermore, in the first and second methods for estimating a remainingcapacity of a secondary battery, it is preferable that characteristicsof a remaining capacity with respect to an electromotive force with atemperature being a parameter are previously obtained, and a remainingcapacity is estimated with reference to a look-up table or a formulastoring the characteristics.

According to the above method, a remaining capacity can be estimatedeasily with good accuracy, even with respect to a temperature change ina battery.

It is preferable that the first and second methods for estimating aremaining capacity of a secondary battery further include the step ofselecting the obtained plurality of data sets based on a predeterminedselection condition, and as the predetermined selection condition, inthe case where the values of currents are in a predetermined range on acharging side and a discharging side, the number of the plurality ofdata sets is a predetermined number or more on the charging side and thedischarging side, and the variation of the accumulated capacity whilethe plurality of data sets are being obtained is in a predeterminedrange, the plurality of data sets are selected.

According to the above method, a plurality of data sets can be obtaineduniformly on the discharging side and the charging side without beinginfluenced by the variation of the accumulated capacity.

It is preferable that the first and second methods for estimating aremaining capacity of a secondary battery further include the step ofdetermining whether or not the calculated no-load voltage is effectivebased on a predetermined determination condition, and as thepredetermined determination condition, in the case where a variance of aplurality of data sets with respect to an approximate line obtained bystatistical processing using least squares is in a predetermined range,or a correlation coefficient between the approximate line and theplurality of data sets is equal to or more than a predetermined value,the calculated no-load voltage is determined to be effective.

According to the above method, the calculation accuracy of a no-loadvoltage can be enhanced.

In the first and second methods for estimating a remaining capacity of asecondary battery, the secondary battery is a nickel-metal hydridesecondary battery.

In order to achieve the above-mentioned object, a second battery packsystem according to the present invention includes a computer system forperforming the first or second method for estimating a remainingcapacity of a secondary battery and a secondary battery.

In order to achieve the above-mentioned object, a battery pack systemincluding a computer system for performing a method for estimating aremaining capacity of a secondary battery and a secondary battery ismounted on a second motor-driven vehicle according to the presentinvention.

According to the above configuration, a battery pack system on which,for example, a battery ECU is mounted as a microcomputer exactlycontrols an SOC based on an SOC estimated with high accuracy, and canrealize an excellent fuel consumption efficiency when mounted on amotor-driven vehicle such as an HEV or the like.

In order to achieve the above-mentioned object, a first apparatus forestimating a remaining capacity of a secondary battery according to thepresent invention includes: a current measuring section for measuring acurrent flowing through a secondary battery as current data; a voltagemeasuring section for measuring a terminal voltage of the secondarybattery corresponding to the current as voltage data; a no-load voltagecalculation section for calculating voltage data in a case where currentdata is zero as a no-load voltage by statistical processing, based on aplurality of data sets of the current data from the current measuringsection and the voltage data from the voltage measuring section; anaccumulated capacity calculation section for calculating an accumulatedcapacity based on current data from the current measuring section; acapacity change calculation section for obtaining a variation of theaccumulated capacity during a predetermined period of time from theaccumulated capacity calculation section; a polarization voltagecalculation section for obtaining a polarization voltage based on thevariation of the accumulated capacity from the capacity changecalculation section; an electromotive force calculation section forsubtracting a polarization voltage obtained in the polarization voltagecalculation section from the no-load voltage calculated in the no-loadvoltage calculation section to calculate an electromotive force of thesecondary battery; and a remaining capacity estimation section forestimating a remaining capacity of the secondary battery based on theelectromotive force from the electromotive force calculation section.

In order to achieve the above-mentioned object, a second apparatus forestimating a remaining capacity of a secondary battery according to thepresent invention includes: a current measuring section for measuring acurrent flowing through a secondary battery used in an intermediatelycharged state as a power source for a motor and a driving source for aload as current data; a voltage measuring section for measuring aterminal voltage of the secondary battery corresponding to the currentas voltage data; a no-load voltage calculation section for calculatingvoltage data in a case where current data is zero as a no-load voltageby statistical processing, based on a plurality of data sets of thecurrent data from the current measuring section and the voltage datafrom the voltage measuring section; an accumulated capacity calculationsection for calculating an accumulated capacity based on current datafrom the current measuring section; a capacity change calculationsection for obtaining a variation of the accumulated capacity during apredetermined period of time from the accumulated capacity calculationsection; a polarization voltage calculation section for obtaining apolarization voltage based on the variation of the accumulated capacityfrom the capacity change calculation section; an electromotive forcecalculation section for subtracting a polarization voltage obtained inthe polarization voltage calculation section from the no-load voltagecalculated in the no-load voltage calculation section to calculate anelectromotive force of the secondary battery; and a remaining capacityestimation section for estimating a remaining capacity of the secondarybattery based on the electromotive force from the electromotive forcecalculation section.

According to the above configuration, since the estimation accuracy of apolarization voltage is satisfactory, the calculation accuracy of abattery electromotive force (equilibrium potential) obtained bysubtracting a polarization voltage from a no-load voltage is enhanced,which enables an SOC to be estimated with high accuracy.

Furthermore, an SOC can be estimated based on an equilibrium potential,so that an SOC after self-discharging due to a battery being left for along period of time and the like also can be estimated, which makes itunnecessary to periodically initialize the SOC.

It is preferable that the first and second apparatuses for estimating aremaining capacity of a secondary battery further include a firstcomputation section for subjecting the variation of the accumulatedcapacity from the capacity change calculation section to time delayprocessing.

According to the above configuration, a polarization voltage having adelay time with respect to the variation of the accumulated capacity canbe estimated following the variation of the accumulated capacity in realtime.

In the first and second apparatuses for estimating a remaining capacityof a secondary battery, it is preferable that the polarization voltagecalculation section multiplies the variation of the accumulated capacitysubjected to the time delay processing in the first computation sectionby a predetermined coefficient to obtain a polarization voltage.

According to the above configuration, a polarization voltage can becalculated easily.

Furthermore, in the first and second apparatuses for estimating aremaining capacity of a secondary battery, it is preferable that thefirst computation section subjects the variation of the accumulatedcapacity to averaging processing by filtering as well as the time delayprocessing.

According to the above configuration, a fluctuation component of theaccumulated capacity that is not required for calculating a polarizationvoltage can be reduced.

It is preferable that the first and second apparatuses for estimating aremaining capacity of a secondary battery further include a secondcomputation section for subjecting a polarization voltage to time delayprocessing.

According to the above configuration, a remaining capacity having adelay time with respect to a polarization voltage can be estimatedfollowing the polarization voltage in real time.

In this case, it is preferable that the second computation sectionperforms averaging processing by filtering as well as time delayprocessing.

According to the above configuration, a fluctuation component of thepolarization voltage that is not required for estimating a remainingcapacity can be reduced.

It is preferable that the first and second apparatuses for estimating aremaining capacity of a secondary battery further include both a firstcomputation section and a second computation section.

It is preferable that the first and second apparatuses for estimating aremaining capacity of a secondary battery further include a temperaturemeasuring section for measuring a temperature of a secondary battery,and the polarization voltage calculation section obtains a polarizationvoltage based on the temperature measured in the temperature measuringsection and a previously obtained look-up table or formula storingcharacteristics of the polarization voltage with respect to thevariation of the accumulated capacity with a temperature being aparameter.

According to the above configuration, a polarization voltage can beobtained easily with good accuracy, even with respect to a temperaturechange in a battery.

Also, it is preferable that the first and second apparatuses forestimating a remaining capacity of a secondary battery further include atemperature measuring section for measuring a temperature of a battery,and the remaining capacity estimation section estimates a remainingcapacity based on the temperature measured in the temperature measuringsection and a previously obtained look-up table or formula storingcharacteristics of the remaining capacity with respect to anelectromotive force with a temperature being a parameter.

According to the above configuration, a remaining capacity can beestimated easily with good accuracy, even with respect to a temperaturechange in a battery.

Also, it is preferable that the first and second apparatuses forestimating a remaining capacity of a secondary batter further include adata set selection section for selecting a plurality of data sets basedon a predetermined selection condition and outputting them to a no-loadvoltage calculation section, and as the predetermined selectioncondition, in the case where the values of currents are in apredetermined range on a charging side and a discharging side, thenumber of the plurality of data sets is a predetermined number or moreon the charging side and the discharging side, and the variation of theaccumulated capacity while the plurality of data sets are being obtainedis in a predetermined range, the data set selection section selects theplurality of data sets.

According to the above configuration, a plurality of data sets can beobtained uniformly on the discharging side and the charging side withoutbeing influenced by the variation of the accumulated capacity.

Also, it is preferable that the first and second apparatuses forestimating a remaining capacity of a secondary battery further include ano-load voltage determination section for determining whether or not ano-load voltage calculated in the no-load voltage calculation section iseffective based on a predetermined determination condition, and as thepredetermined determination condition, in the case where a variance of aplurality of data sets with respect to an approximate line obtained bystatistical processing using least squares is in a predetermined range,or a correlation coefficient between the approximate line and theplurality of data sets is equal to or more than a predetermined value,the calculated no-load voltage is determined to be effective.

According to the above configuration, the calculation accuracy of ano-load voltage can be enhanced.

In the first and second apparatuses for estimating a remaining capacityof a secondary battery, the secondary battery is a nickel-metal hydridesecondary battery.

In order to achieve the above-mentioned object, a third battery packsystem according to the present invention includes a first or secondapparatus for estimating a remaining capacity of a secondary battery anda secondary battery. In this case, it is preferable that the first andsecond apparatuses for estimating a remaining capacity of a secondarybattery is configured as a computer system.

In order to achieve the above-mentioned object, a battery pack systemincluding the second apparatus for estimating a remaining capacity of asecondary battery and a secondary battery is mounted on a thirdmotor-driven vehicle according to the present invention. In this case,it is preferable that the second apparatus for estimating a remainingcapacity of a secondary battery is configured as a computer system.

According to the above configuration, the battery pack system on which abattery ECU, for example, is mounted as a microcomputer system cancontrol an SOC exactly based on an SOC estimated with high accuracy, andrealize an excellent fuel consumption efficiency when mounted on amotor-driven vehicle such as an HEV and the like.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram showing an exemplary configuration of abattery pack system according to one embodiment of the presentinvention.

FIG. 2 is a diagram showing an example of a variation ΔQ of anaccumulated capacity and a change in a polarization voltage Vpol withthe passage of time.

FIG. 3 is a diagram showing a characteristic curve of a polarizationvoltage Vpol with respect to a variation LPF (ΔQ) of an accumulatedcapacity after filtering, with a temperature being a parameter, in thepresent embodiment.

FIG. 4 is a diagram showing data sets of voltage data V(n) and currentdata I(n) and an approximate line for obtaining a no-load voltage V0from the data sets by statistical processing in the present embodiment.

FIG. 5 is a diagram showing a characteristic curve of an electromotiveforce Veq with respect to a remaining capacity SOC, with a temperaturebeing a parameter, in the present embodiment.

FIG. 6 is a flow chart showing a processing procedure in a method forestimating a remaining capacity of a secondary battery according to thepresent embodiment.

FIG. 7 is a diagram showing a change with the passage of time in aremaining capacity SOCp estimated in the present embodiment (in the casewhere a variation ΔQ of an accumulated capacity is not filtered), aremaining capacity SOCc estimated from a no-load voltage V0 in aconventional example, and a true remaining capacity SOCt.

FIG. 8 is a diagram showing a change with the passage of time in aremaining capacity SOCp (LPF) estimated in the present embodiment (inthe case where a variation ΔQ of an accumulated capacity is filtered),and a true remaining capacity SOCt.

FIG. 9 is a diagram showing a true Veq-SOC curve (P0), and electromotiveforce-SOC plotted data in the case where a remaining capacity isestimated in the present embodiment (P1: in the case where a variationΔQ of an accumulated capacity is not filtered) and in the case where aremaining capacity is estimated from a no-load voltage V0 in theconventional example (P2).

FIG. 10 is a diagram showing a true Veq-SOC curve (P0), andelectromotive force-SOC plotted data in the case where a remainingcapacity is estimated in the present embodiment (P1 (LPF): in the casewhere a variation ΔQ of an accumulated capacity is filtered) and in thecase where a remaining capacity is estimated from a no-load voltage V0in the conventional example (P2).

FIG. 11 is a block diagram showing a battery pack system 1 used in ahybrid electric vehicle (HEV) 2. The HEV 2 is provided with an engine 4and a motor 5 for rotating wheels 3. The battery pack system 1 includessecondary battery 100 and an electronic control unit for a battery(battery ECU) 101. Charging/discharging of the secondary battery 100 iscontrolled by the battery ECU 101. An electric generator 6 is drivenwith surplus motive power trough a transmission 7 to charge a secondarybattery 100 through a controller 9.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, the present invention will be described by way of preferredembodiments with reference to the drawings.

FIG. 1 is a block diagram showing an exemplary configuration of abattery pack system according to one embodiment of the presentinvention. In FIG. 1, a battery pack system 1 is composed of a secondarybattery 100 in which a plurality of cells are combined, and a batteryECU 101 including an apparatus for estimating a remaining capacityaccording to the present invention, as a part of a microcomputer system.

In the battery ECU 101, reference numeral 102 denotes a voltagemeasuring section for measuring a terminal voltage of the secondarybattery 100 detected by a voltage sensor (not shown) at a predeterminedsampling period as voltage data V(n), 103 denotes a current measuringsection for measuring a charging/discharging current of the secondarybattery 100 detected by the current sensor (not shown) at apredetermined sampling as current data I(n) (the sign of whichrepresents either a charging direction or a discharging direction), and104 denotes a temperature measuring section for measuring a temperatureof the secondary battery 100 detected by the temperature sensor (notshown) as temperature data T(n).

The current data I(n) from the current measuring section 103 is input toan accumulated capacity calculation section 105, and an accumulatedcapacity Q during a predetermined period of time is calculated. Theaccumulated capacity Q calculated in the accumulated capacitycalculation section 105 is input to a capacity change calculationsection 106, and a variation ΔQ of the accumulated capacity Q during apredetermined period of time (e.g., one minute) is obtained. Thevariation ΔQ of the accumulated capacity is input to a first computationsection 107 that functions as a low-pass filter (LPF). In the firstcomputation section 107, time delay processing for adjusting the timingbetween the variation ΔQ of the accumulated capacity and thepolarization voltage obtained in a subsequent polarization voltagecalculation section 108 and averaging processing for removing afluctuation component corresponding to an unnecessary high-frequencycomponent are performed, and the result is output as LPF (ΔQ). Herein,FIG. 2 shows, as an example, a variation ΔQ of an accumulated capacityduring the past one minute as a solid line, and a polarization voltageVpol as a broken line. It is understood from FIG. 2 that thepolarization voltage Vpol is changed after tens of seconds from thevariation ΔQ of the accumulated capacity during the past one minute.Corresponding to this time delay, a time constant τ of the LPF (in thepresent embodiment, the LPF is composed of a primary delay element)constituting the first computation section 107 is determined.

The LPF (ΔQ) from the first computation section 107 is input to thepolarization voltage calculation section 108. In the polarizationvoltage calculation section 108, the polarization voltage Vpol iscalculated based on the temperature data T(n) measured in thetemperature measuring part 104, from a characteristic curve or a formulaof the polarization voltage Vpol with respect to the LPF (ΔQ) with atemperature being a parameter, previously stored in a look-up table(LUT) 1081. Herein, FIG. 3 shows a characteristic curve of thepolarization voltage Vpol with respect to the LPF (ΔQ) in the case wherethe temperature is 25° C. FIG. 3 shows only the characteristic curve inthe case of 25° C. However, actually, in the case of the application toan HEV, for example, characteristic curves that can cover a range from−30° C. to +60° C. are stored in the LUT 1081 as look-up data.

The polarization voltage Vpol obtained in the polarization voltagecalculation section 108 is input to a second computation section 109that functions as a low-pass filter (LPF). In the second computationsection 109, time delay processing for adjusting the timing between thepolarization voltage Vpol and an electromotive force Veq obtained in asubsequent electromotive force calculation section 113 and averagingprocessing for removing a fluctuation component corresponding to anunnecessary high-frequency component are performed, and the result isoutput as LPF (Vpol).

Furthermore, the voltage data V(n) from the voltage measuring section102 and the current data I(n) from the current measuring section 103 areinput to a data set selection section 110 as data sets. In the data setselection section 110, as a selection condition, in the case where thevalues of the current data I(n) in a charging direction (−) and adischarging direction (+) are in a predetermined range (e.g., ±50 A),there are a predetermined number or more (e.g., each 10 among 60samples) of current data I(n) in the charging direction and thedischarging direction, and the variation ΔQ of the accumulated capacitywhile data sets are being obtained is in a predetermined range (e.g.,0.3 Ah), the data sets of the voltage data V(n) and the current dataI(n) are determined to be effective, and they are selected and output aseffective data sets S (V(n), I(n)).

The effective data sets S(V(n), I(n)) from the data set selectionsection 110 are input to a no-load voltage calculation section 111. Inthe no-load voltage calculation section 111, as shown in FIG. 4, aprimary voltage-current line (approximate line) is obtained from theeffective data sets S(V(n), I(n)) by statistical processing using leastsquares, and a voltage value (voltage (V) intercept) corresponding to 0current is calculated as a no-load voltage V0.

The no-load voltage V0 from the no-load voltage calculation section 111is input to a no-load voltage determination section 112. In the no-loadvoltage determination section 112, in the case where as a determinationcondition, a variance of the data sets S(V(n), I(n)) with respect to theapproximate line is obtained and this variance is in a predeterminedrange, or a correlation coefficient between the approximate line and thedata sets S(V(n), I(n)) is obtained and this correlation coefficient isa predetermined value or more, the calculated no-load voltage V0 isdetermined to be effective, and output as an effective no-load voltageV0 _(OK).

Next, the electromotive force calculation section 113 subtracts thepolarization voltage LPF (Vpol) after filtering from the secondcomputation section 109, from the effective no-load voltage V0 _(OK)from the no-load voltage determination section 112, as described above,thereby calculating an electromotive force Veq (equilibrium potential).The electromotive force Veq thus calculated is input to a remainingcapacity estimation section 114. In the remaining capacity estimationsection 114, a remaining capacity SOC is estimated based on thetemperature data T(n) measured in the temperature measuring section 104,from a characteristic curve or a formula of the electromotive force Veqwith respect to the remaining capacity SOC with a temperature being aparameter, previously stored in a look-up table (LUT) 1141. Herein, FIG.5 shows a characteristic curve of the electromotive force Veq withrespect to the remaining capacity SOC in the case of a temperature of25° C. FIG. 5 shows only a characteristic curve in the case of 25° C.However, actually, in the case of the application to an HEV, forexample, characteristic curves that can cover a range of −30° C. to +60°C. are stored in the LUT 1141 as look-up data.

Next, a processing procedure of estimating a remaining capacity in abattery pack system configured as described above will be described withreference to FIG. 6.

FIG. 6 is a flow chart showing a processing procedure in a method forestimating a remaining capacity of a secondary battery according to oneembodiment of the present invention. In FIG. 6, voltage data V(n) andcurrent data I(n) are measured as data sets (S601). Then, an accumulatedcapacity Q is calculated by accumulating currents, based on the currentdata I(n) (S602). Then, a variation ΔQ of the accumulated capacity Qduring a predetermined period of time (e.g., one minute) is calculated(S603). Then, the variation ΔQ of the accumulated capacity is filtered(time delay and averaging processing) to compute LPF (ΔQ) (S604). Then,a polarization voltage Vpol is calculated with reference to a look-uptable previously storing polarization voltage Vpol-LPF (ΔQ)characteristic data, with the temperature data T(n) being a parameter,from the computed LPF (ΔQ) (S605). The above-mentioned Steps S601 toS605 are the processing procedure in a method for estimating apolarization voltage of the present invention. Then, the calculatedpolarization voltage Vpol is filtered (time delay and averagingprocessing), thereby computing LPF (Vpol) (S606).

Furthermore, in order to examine whether or not the data sets of thevoltage data V(n) and the current data I(n) measured in Step S601 areeffective, it is determined whether or not these data sets satisfy theselection condition as described above (S607). In the case where thedata sets do not satisfy the selection condition in the determination inStep S607 (No), the process returns to Step S601, and the data sets ofthe voltage data V(n) and the current data I(n) are measured again. Onthe other hand, in the case where the data sets satisfy the selectioncondition in the determination in Step S607 (Yes), the process proceedsto Step S608, and a plurality of (e.g., each 10 in the charging anddischarging directions among 60 samples) effective data sets S(V(n),I(n)) are obtained (S608).

Next, a primary approximate line (V-I line) is obtained from theeffective data sets S(V(n), I(n)) by statistical processing using leastsquares. A V intercept of the approximate line is calculated as ano-load voltage V0 (S609). Then, in order to examine whether or not theno-load voltage V0 calculated in Step S609 is effective, it isdetermined whether or not the no-load voltage V0 satisfies theabove-mentioned determination condition. In the case where the no-loadvoltage V0 does not satisfy the determination condition in thedetermination in Step S610 (No), the process returns to Step S608. Then,another plurality of (e.g., a different set of 10 among 60 samples)effective data sets S(V(n), I(n)) are obtained, and Steps S609 and S610are repeated. On the other hand, in the case where the calculatedno-load voltage V0 satisfies the determination condition in thedetermination in Step S610, the calculated no-load voltage V0 is set tobe an effective no-load voltage V0 _(OK).

Thus, an electromotive force Veq of a battery is obtained from theobtained polarization voltage LPF (Vpol) after filtering and theobtained effective no-load voltage V0 _(OK). The electromotive force Veqis calculated by subtracting the polarization voltage LPF (Vpol) afterfiltering from the effective no-load voltage V₀ _(OK). Next, a remainingcapacity SOC is estimated with reference to a look-up table previouslystoring an electromotive force Veq-remaining capacity SOC characteristicdata with the temperature data T(n) being a parameter, from thecalculated electromotive force Veq (S612).

Next, the accuracy of the remaining capacity SOC estimated as describedabove will be described with reference to FIGS. 7 and 8, with respect tothe case where the filtering in the first computation section 107 andthe second computation section 109 shown in FIG. 1 and in Steps S604 andStep 606 shown in FIG. 2 is not performed, and the case where thefiltering in the first computation section 107 and Step S604 isperformed.

FIG. 7 is a diagram showing a change with the passage of time in aremaining capacity SOCp estimated in the present embodiment, a remainingcapacity SOCc estimated from a no-load voltage V₀ in a conventionalexample, and a true remaining capacity SOCt. As shown in FIG. 7,according to the conventional estimation method, there is a deviation ofat most 10% or more with respect to the true remaining capacity SOCt;however, the remaining capacity SOCp estimated in the present embodimenthas a deviation of 4% or less. Thus, the estimation accuracy of theremaining capacity SOC can be enhanced by 2.5 times or more.Particularly, in the case where the remaining capacity SOC is changedlargely with the passage of time (for example, 1800 seconds to 2750seconds in FIG. 7), according to the conventional example, there is adeviation of −10% to +12% (the range of a deviation is 22%) with respectto the true remaining capacity SOCt; however, according to the presentembodiment, the deviation can be suppressed to be in a range of −2% to−4% (the range of a deviation is 4%). Thus, the estimation accuracy ofthe remaining capacity SOC can be enhanced further.

FIG. 8 is a diagram showing a change with the passage of time in aremaining capacity SOCp (LPF) estimated in the present embodiment, and atrue remaining capacity SOCt. As shown in FIG. 8, the variation ΔQ ofthe accumulated capacity is filtered, whereby the deviation of theremaining capacity SOCp can be suppressed to 2% or less with respect tothe true remaining capacity SOCt, and the estimation accuracy of theremaining capacity SOC can be enhanced by 5 times or more compared withthe conventional example.

FIGS. 9 and 10 respectively are diagrams showing a true electromotiveforce Veq-remaining capacity SOC curve (P0), and electromotive forceVeq-remaining capacity SOC plotted data in the case where a remainingcapacity is estimated in the present embodiment (P1 and P1 (LPF)) and inthe case where a remaining capacity is estimated from a no-load voltageV0 in a conventional example (P2).

As shown in FIG. 9, in the intermediate remaining capacity range (about45% to about 75%) used in the application to an HEV, the variation ofplotted data with respect to the true electromotive force Veq-remainingcapacity SOC curve P0 is smaller in the present embodiment, comparedwith the conventional example. Furthermore, as shown in FIG. 10, in thecase where the variation ΔQ of the accumulated capacity is filtered, theaccuracy is further enhanced.

In the present embodiment, a predetermined period of time forcalculating the variation ΔQ of the accumulated capacity is set to be,for example, one minute. However, the predetermined period of time maybe varied in accordance with the driving state of a vehicle, in the casewhere the battery pack system is mounted on an HEV or the like. Morespecifically, the predetermined period of time is set to be short in thecase where a secondary battery is charged/discharged frequently, and thepredetermined period of time is set to be long in the case where thesecondary battery is not charged/discharged frequently. Thus, apolarization voltage can be estimated optimally in accordance with anactual driving state.

Furthermore, in the present embodiment, a computation section is dividedinto the first computation section 107 and the second computationsection 109 so as to perform filtering. They may be combined into one,if required. This can reduce the processing steps, and enhance theprocessing speed.

In the present embodiment, the polarization voltage is calculated in theabsence of a load where there is no component resistance. However, acomponent resistance that can be previously measured easily is tabulatedin advance and taken into consideration, whereby the polarizationvoltage and SOC can be calculated exactly in a similar manner evenduring a period of time other than a no-load period.

As described above, according to the present invention, the polarizationvoltage is obtained from the variation of the accumulated capacity,whereby the estimation accuracy of the polarization voltage is enhanced,and the calculation accuracy of a battery electromotive force(equilibrium potential) obtained by subtracting the polarization voltagefrom the no-load voltage is enhanced. Consequently, an SOC can beestimated with high accuracy.

Furthermore, the SOC can be estimated based on the equilibriumpotential. Therefore, the SOC after self-discharging when being left fora long period of time, and the like can be estimated easily, which makesit unnecessary to periodically initialize the SOC.

1. A method for estimating a polarization voltage of a secondarybattery, comprising the steps of: measuring a current flowing through asecondary battery; calculating a first accumulated capacity byaccumulating the measured current over a predetermined period of time;calculating a second accumulated capacity by accumulating the measuredcurrent over a next predetermined period of time; calculating adifference between the first accumulated capacity and the secondaccumulated capacity to obtain a variation of the calculated accumulatedcapacity; and obtaining a polarization voltage based on the variation ofthe accumulated capacity.
 2. A method for estimating a polarizationvoltage of a secondary battery, comprising the steps of: measuring acurrent flowing through a secondary battery used in an intermediatelycharged state as a power source for a motor and a driving source for aload; calculating a first accumulated capacity by accumulating themeasured current over a predetermined period of time; calculating asecond accumulated capacity by accumulating the measured current over anext predetermined period of time; calculating a difference between thefirst accumulated capacity and the second accumulated capacity to obtaina variation of the accumulated capacity; and obtaining a polarizationvoltage based on the variation of the accumulated capacity.
 3. A batterypack system, comprising: a secondary battery; and an electric controlunit for a battery (battery ECU) for estimating a polarization voltageof the secondary battery, wherein the electric control unit isconfigured to measure a current flowing through a secondary battery,calculate a first accumulated capacity by accumulating the measuredcurrent over a predetermined period of time, calculate a secondaccumulated capacity by accumulating the measured current over a nextpredetermined period of time, calculate a difference between the firstaccumulated capacity and the second accumulated capacity to obtain avariation of the accumulated capacity, and obtain a polarization voltagebased on the variation of the accumulated capacity.
 4. A motor-drivenvehicle, comprising: a battery pack system mounted on a motor, thebattery pack system comprising a secondary battery and a battery ECU forestimating a polarization voltage of the secondary battery, wherein thebattery ECU is configured to measure a current flowing through asecondary battery, calculate a first accumulated capacity byaccumulating the measured current over a predetermined period of time,calculate a second accumulated capacity by accumulating the measuredcurrent over a next predetermined period of time, calculate a differencebetween the first accumulated capacity and the second accumulatedcapacity to obtain a variation of the accumulated capacity, and obtain apolarization voltage based on the variation of the accumulated capacity.5. A method for estimating a remaining capacity of a secondary battery,comprising the steps of: measuring a data set of a current flowingthrough a secondary battery and a terminal voltage of the secondarybattery corresponding to the current, and obtaining a plurality of thedata sets; calculating a voltage value in a case where a current valueis zero based on the obtained plurality of data sets by statisticalprocessing as a no-load voltage; calculating a first accumulatedcapacity during a predetermined period of time based on the measuredcurrent; calculating a second accumulated capacity during a nextpredetermined period of time based on the measured current; calculatinga difference between the first accumulated capacity and the secondaccumulated capacity to obtain a variation of the accumulated capacity;obtaining a polarization voltage based on the variation of theaccumulated capacity; subtracting the polarization voltage from theno-load voltage to calculate an electromotive force of the secondarybattery; and estimating a remaining capacity of the secondary batterybased on the calculated electromotive force.
 6. A method for estimatinga remaining capacity of a secondary battery, comprising the steps of:measuring a data set of a current flowing through a secondary batteryused in an intermediately charged state as a power source for a motorand a driving source for a load, and a terminal voltage of the secondarybattery corresponding to the current to obtain a plurality of the datasets; calculating a voltage value in a case where a current value iszero based on the obtained plurality of data sets by statisticalprocessing as a no-load voltage; calculating a first accumulatedcapacity during a predetermined period of time based on the measuredcurrent; calculating a second accumulated capacity during a nextpredetermined period of time based on the measured current; calculatinga difference between the first accumulated capacity and the secondaccumulated capacity to obtain a variation of the calculated accumulatedcapacity; obtaining a polarization voltage based on the variation of theaccumulated capacity; subtracting the polarization voltage from theno-load voltage to calculate an electromotive force of the secondarybattery; and estimating a remaining capacity of the secondary batterybased on the calculated electromotive force.
 7. A battery pack system,comprising: a secondary battery; and a battery ECU for estimating aremaining capacity of the secondary battery, wherein the battery ECU isconfigured to measure a data set of a current flowing through asecondary battery and a terminal voltage of the secondary batterycorresponding to the current, and obtaining a plurality of the datasets, calculate a voltage value in a case where a current value is zerobased on the obtained plurality of data sets by statistical processingas a no-load voltage, calculate a first accumulated capacity during apredetermined period of time based on the measured current, calculate asecond accumulated capacity during a next predetermined period of timebased on the measured current, calculate a difference between the firstaccumulated capacity and the second accumulated capacity to obtain avariation of the accumulated capacity, obtain a polarization voltagebased on the variation of the accumulated capacity, subtract thepolarization voltage from the no-load voltage to calculate anelectromotive force of the secondary battery, and estimate a remainingcapacity of the secondary battery based on the calculated electromotiveforce.
 8. A motor-driven vehicle comprising: a battery pack systemmounted on a motor, the battery pack system comprising a secondarybattery and a battery ECU for estimating a remaining capacity of thesecondary battery, wherein the battery ECU is configured to measure adata set of a current flowing through a secondary battery used in anintermediately charged state as a power source for a motor and a drivingsource for a load, and a terminal voltage of the secondary batterycorresponding to the current to obtain a plurality of the data sets,calculate a voltage value in a case where a current value is zero basedon the obtained plurality of data sets by statistical processing as ano-load voltage, calculate a first accumulated capacity during apredetermined period of time based on the measured current, calculate asecond accumulated capacity during a next predetermined period of timebased on the measured current, calculate a difference between the firstaccumulated capacity and the second accumulated capacity to obtain avariation of the accumulated capacity, obtain a polarization voltagebased on the variation of the accumulated capacity, subtract thepolarization voltage from the no-load voltage to calculate anelectromotive force of the secondary battery, and estimate a remainingcapacity of the secondary battery based on the calculated electromotiveforce.
 9. An apparatus for estimating a remaining capacity of asecondary battery, comprising: an electric current measuring section formeasuring an electric current flowing through a secondary battery ascurrent data; a voltage measuring section for measuring a terminalvoltage of the secondary battery corresponding to the current as voltagedata; a no-load voltage calculation section for calculating voltage datain a case where current data is zero as a no-load voltage by statisticalprocessing, based on a plurality of data sets of the current data fromthe electric current measuring section and the voltage data from thevoltage measuring section; an accumulated capacity calculation sectionfor calculating a first accumulated capacity during a predeterminedperiod of time and a second accumulated capacity during a nextpredetermined period of time based on current data from the electriccurrent measuring section and; a capacity change calculation section forcalculating a difference between the first accumulated capacity and thesecond accumulated capacity to obtain a variation of the accumulatedcapacity; a polarization voltage calculation section for obtaining apolarization voltage based on the variation of the accumulated capacityfrom the capacity change calculation section; an electromotive forcecalculation section for subtracting a polarization voltage obtained inthe polarization voltage calculation section from the no-load voltagecalculated in the no-load voltage calculation section to calculate anelectromotive force of the secondary battery; and a remaining capacityestimation section for estimating a remaining capacity of the secondarybattery based on the electromotive force from the electromotive forcecalculation section.
 10. An apparatus for estimating a remainingcapacity of a secondary battery, comprising: a current measuring sectionfor measuring a current flowing through a secondary battery used in anintermediately charged state as a power source for a motor and a drivingsource for a load as current data; a voltage measuring section formeasuring a terminal voltage of the secondary battery corresponding tothe current as voltage data; a no-load voltage calculation section forcalculating voltage data in a case where current data is zero as ano-load voltage by statistical processing, based on a plurality of datasets of the current data from the current measuring section and thevoltage data from the voltage measuring section; an accumulated capacitycalculation section for calculating a first accumulated capacity duringa predetermined period of time and a second accumulated capacity duringa next predetermined period of time based on current data from thecurrent measuring section; a capacity change calculation section forcalculating a difference between the first accumulated capacity and thesecond accumulated capacity to obtain a variation of the accumulatedcapacity; a polarization voltage calculation section for obtaining apolarization voltage based on the variation of the accumulated capacityfrom the capacity change calculation section; an electromotive forcecalculation section for subtracting a polarization voltage obtained inthe polarization voltage calculation section from the no-load voltagecalculated in the no-load voltage calculation section to calculate anelectromotive force of the secondary battery; and a remaining capacityestimation section for estimating a remaining capacity of the secondarybattery based on the electromotive force from the electromotive forcecalculation section.
 11. The apparatus according to claim 10, whereinthe apparatus for estimating a remaining capacity of a secondary batteryis configured as a battery ECU in a motor driven vehicle.
 12. A batterypack system, comprising: a secondary battery; and a battery ECU forestimating a polarization voltage of the secondary battery, wherein thebattery ECU is configured to measure a current flowing through asecondary battery used in an intermediately charged state as a powersource for a motor and a driving source for a load, calculate a firstaccumulated capacity by accumulating the measured current over apredetermined period of time, calculate a second accumulated capacity byaccumulating the measured current over a next predetermined period oftime, calculate a difference between the first accumulated capacity andthe second accumulated capacity to obtain a variation of the accumulatedcapacity, and obtain a polarization voltage based on the variation ofthe accumulated capacity.
 13. A battery pack system, comprising: asecondary battery; and a battery ECU for estimating a remaining capacityof the secondary battery, wherein the battery ECU is configured tomeasure a data set of a current flowing through a secondary battery usedin an intermediately charged state as a power source for a motor and adriving source for a load, and a terminal voltage of the secondarybattery corresponding to the current to obtain a plurality of the datasets, calculate a voltage value in a case where a current value is zerobased on the obtained plurality of data sets by statistical processingas a no-load voltage, calculate a first accumulated capacity during apredetermined period of time based on the measured current, calculate asecond accumulated capacity during a next predetermined period of timebased on the measured current, calculate a difference between the firstaccumulated capacity and the second accumulated capacity to obtain avariation of the accumulated capacity, obtain a polarization voltagebased on the variation of the accumulated capacity, subtract thepolarization voltage from the no-load voltage to calculate anelectromotive force of the secondary battery, and estimate a remainingcapacity of the secondary battery based on the calculated electromotiveforce.
 14. A battery pack system, comprising: the apparatus forestimating a remaining capacity of a secondary battery of claim 10; andthe secondary battery.
 15. The battery pack system according to claim14, wherein the apparatus for estimating a remaining capacity of asecondary battery is configured as a battery ECU.
 16. A battery packsystem, comprising: the apparatus estimating a remaining capacity of asecondary battery of claim 9; and the secondary battery.
 17. The batterypack system according to claim 16, wherein the apparatus for estimatinga remaining capacity of a secondary battery is configured as a batteryECU.
 18. The motor-driven vehicle on which a battery pack systemcomprising the apparatus for estimating a remaining capacity of asecondary battery of claim 10 and the secondary battery is mounted.